Empirical methods explore the statistical relationships between image pixel values and field measured water depths.

Analytical approaches rely on the general principle that sea water transmittances at near-visible wavelengths are functions of a general optical equation dependent on the intrisinc optical properties of sea water. A number of external factors affect the accuracy of the depth calculation, including the spatial and spectral resolution of the imagery, the viewing angle of the satellite, the solar illumination angle, atmospheric effects, sunlight, tide level and submerged vegetation. Careful selection of satellite imagery and subsequent image processing can mitigate some of these effects.

Anything in between? YES, see 4SM

4SM is an empirical "ratio method" operating a radiance inversion approachwhich does not need any field measured water depths for calibration

which relies on an understanding of the physics behind

which requires the practioner to maintain physical consistency among parameters

rather than rely on existing depth measurements and multiple regressions

which assumes homogeneous atmospheric and water optical properties

which, being a ratio method, does not need conversion of TOA DN radiances into BOA reflectance

which uses bareland pixels in the image to specify the agronomer's Soil Line concept

as a spectral reference for shallow pixels pixels at null depth

this then leads to approximate estimation of the spectral atmospheric path radiance: no need for formal atmospheric correction,

uses the "dark pixel" assumption

which requires proper removal of sea-surface clutter (glint)

which relies on the estimation of spectral opticaly deep water radiance from the image

which relies on measuring the ratio KBLUE/KGREENfrom shallow areas of the image, as proposed by Lyzenga

which uses Jerlov's table of diffuse attenuation coefficients of marine waters for specifying spectral K in the visible range as a function on the ratioKBLUE/KGREENobserved for the shallow areas of the image, as observed by Kirk.

which uses a visual display of the optical calibration diagram as a powerful tool to ascertain physical consistency of all parameters

4SM operates the "simplified radiative transfer equation" as suggested by Maritorena, Morel and Gentilly, 1994, under the proviso that both atmosphere and water column are homogeneous over the ROI, vertically ans spatially, and that sea-surface clutter has been removed (sun/sky glint).

this means that most of the atmospheric/water_column complexities involved in analytical methods are rounded up into two variables:

a TOA spectral Lsw deep water radiance term or a BOA Lw deep water radiance term

a spectral two-ways diffuse attenuation coefficient 2K term in units of 1/m

therefore, the spectral TOA signal is Ls=Lsw+LsB-Lsw)/exp(2K_Z) in units of image DNs

Note from Sachak Pe'eri, NOAA, 2015"For an algorithm that can be used by the hydrographic community on a COTS GIS software, a ratio transform algorithm based from an optimization approach provides a robust solution that does not require to sample the environment or generate a database. "this applies to 4SM